North Yorkshire Fire and Rescue Service received the call about the incident at 6.11pm.
Crews from Pickering, Whitby, Robin Hoods Bay and RAF Fylingdales extinguished the fire, which left the driver with minor burns on their hands.
No one else suffered any injuries and the driver was treated at the scene by the fire service.
Crews used six breathing apparatus, five hose reels and small tools to make the vehicle safe.